Chaotic dynamics in Cournot duopoly model with bounded rationality based on relative profit delegation maximization

In this paper, we maximize the utility function under budget constraint in an oligopoly market. We consider a Cournot duopoly model with boundedly rational players adopting the gradient adjustment mechanism to update their productions. The dynamics of Cournot duopoly model with relative profit delegation maximization is analyzed. We explore the local stability of Nash equilibrium point and the occurrence of complexity behaviors. Additionally, the chaotic dynamics of this game via flip bifurcations and Neimark–Sacker bifurcations are researched. Numerical simulations are presented to show bifurcation diagrams, sensitive dependence on initial conditions, strange attractors and chaos. As to the fractal structure emerged in evolution process, the fractal dimension is calculated. Further analysis of the simulation results indicates that the chaotic behavior of the system can be stabilized on the Nash equilibrium point by using state variables feedback and parameter variation method.